Magnetic recording and reproduction apparatus

ABSTRACT

A magnetic recording and reproduction apparatus, includes a circuit for changing a reference amplitude value of a Viterbi detector. The circuit is used to record and reproduce data with the reference amplitude value displaced from a reference value, thereby measuring the data error rate. Displacement of the reference amplitude from a reference value increases the data error rate, and therefore the data error rate can be measured within a short time. A data error rate with the reference amplitude equal to a reference value is estimated from the data error rate measurement, thereby making it possible to evaluate the degree of accuracy of a magnetic recording and reproduction apparatus. The data error rate is measured with the reference amplitude of the Viterbi detector displaced from a reference value while changing the equalization coefficient value of a waveform equalizer, the cut-off frequency of a low-pass filter and the write precompensation amount of a write precompensation circuit. In this way, the effect of the reproduction channel parameter or the write precompensation amount on the degree of accuracy of the magnetic recording and reproduction apparatus is evaluated, and the optimum value of the reproduction channel parameter or the write precompensation amount can thus be determined.

This is a continuation application of U.S. Ser. No. 09/435,779, filedNov. 8, 1999, now U.S. Pat. No. 6,175,460 which is a continuationapplication of U.S. Ser. No. 08/529,400, filed Sep. 18, 1995, now U.S.Pat. No. 6,046,873.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a magnetic recording and reproductionapparatus, and more particularly to a magnetic recording andreproduction apparatus having means for evaluating the degree of dataaccuracy and means for detecting a fault to assure the quality of theapparatus.

2. Description of the Related Art

A magnetic recording and reproduction apparatus having a Viterbidetector is described in IEEE Transactions on Magnetics, Vol. 27, pp.4538-4543.

This magnetic recording and reproduction apparatus is made up of a writeprecompensation circuit for correcting a bit shift which is generated atthe time of reproduction, a low-pass filter for removing high-frequencynoise components of an analog reproduction waveform signal read from amagnetic recording medium, an A/D converter for converting the analogreproduction waveform signal into a digital waveform signal, a waveformequalizer for shaping the digital waveform signal, and a Viterbidetector for identifying digital data from the shaped ditigal waveformsignal. In this apparatus, a recording-reproduction signal processingcircuit is contained in a one-chip LSI (Large Scale Integrated Circuit)to meet requirements for reduction in size and increase in data transferrate.

A criterion for deciding the quality of a magnetic recording andreproduction apparatus is the degree of data accuracy. The degree ofdata accuracy is dependent on the recording-reproduction channelparameters such as the amount of write precompensation of the writeprecompensation circuit, the cut-off frequency of the low-pass filter,and the equalization coefficient value of the waveform equalizer, aswell as the electromagnetic conversion characteristics of a magnetichead and a magnetic medium. For producing a magnetic recording andreproduction apparatus of high quality, these parameters are required tobe set to optimum values at the time of using the apparatus. In order todetermine the optimum value of these parameters, on the other hand, thedegree of data accuracy is required to be evaluated quantitatively atthe time of parameter variations.

Generally, an error rate is used as a numerical value for quantifyingthe degree of data accuracy. When a magnetic recording and reproductionapparatus is being used under normal operating conditions, however, theerror rate is so small that the measurement of the error rate requires agreat amount of time, thereby making it difficult to decide the qualityof the apparatus accurately.

JP-A-3-144969 discloses a technique in which the degree of data accuracyis evaluated by comparing the series of a digital waveform signal withthe series of a reference signal, measuring the histogram of theresulted error value, and thus predicting the data error rate of themagnetic recording and reproduction apparatus.

On the other hand, as a conventional method of evaluating the degree ofdata accuracy, a level margin test is known. In the level margin test, agate slice level to be compared with the amplitude of an output signalof the waveform equalizer is moved vertically, and by detecting missingbits or extra bits, the margin width of the gate slice level and thedata error rate are measured.

SUMMARY OF THE INVENTION

The method of predicting an error rate by histogram measurement,however, emphasizes only the distribution of a digital waveform signaland fails to incorporate the data identification characteristics of theViterbi detector for estimating a series of maximum likelihood values.The level margin test, which detects a level for each bit, also does notincorporate the data identification characteristics of a Viterbidetector for estimating a series of maximum likelihood values. For thesereasons, the conventional methods of evaluating the degree of dataaccuracy cannot correctly evaluate the performance of therecording-reproduction channel including the Viterbi detector.

In the case where a recording-reproduction signal processing circuit isbuilt in an LSI chip, it is not easy to detect an optimum value of aparameter unless the same chip includes means for evaluating thedependency of the magnetic recording and reproduction apparatus on therecording-reproduction channel parameters. Further, it is also not easyto determine the quality of the magnetic recording and reproductionapparatus.

An object of the invention is to provide a magnetic recording andreproduction apparatus having a Viterbi detector capable of evaluatingthe degree of data accuracy of the apparatus.

Another object of the invention is to provide a magnetic recording andreproduction apparatus capable of evaluating the degree of data accuracyof the apparatus by changing the circuit characteristics of theapparatus.

Still another object of the invention is to provide a magnetic recordingand reproduction apparatus capable of measuring the data error rate inaccordance with a predetermined sequence.

In order to achieve these objects, according to one aspect of theinvention, there is provided a magnetic recording and reproductionapparatus made up of a data generator for generating write data, a writeprecompensation circuit for correcting the phase of the write datasignal generated from the data generator, and a magnetic head forelectromagnetically converting the write data signal corrected by thewrite precompensation circuit, a magnetic disc moved relatively with themagnetic head for recording and reproducing a signal through themagnetic head, a read-write amplifier amplifies the signal recorded inthe magnetic head and read from the magnetic head, and an AGC circuitkeeps constant the amplitude of the output signal of the read-writeamplifier. The apparatus further includes a low-pass filter for removingthe high-frequency noise components of the output signal of the AGCcircuit, an A/D converter for sampling the output signal of the low-passfilter and converting it into a multi-valued digital value, a waveformequalizer for shaping the digital signal converted by the A/D converter,and a VFO circuit for producing a sample clock of the A/D converter, AViterib detector identifies the output signal of the waveform equalizerby two threshold values and produces read data based on the sampleclock. The apparatus further employs and means for changing thereference amplitude value providing the threshold level of the Viterbidetector, means for comparing the write data and the read data, andmeans for detecting an error, wherein data is recorded and reproducedwith the reference amplitude value changed. The degree of data accuracyof the magnetic recording and reproduction apparatus is evaluatedaccording to the data error rate of the apparatus which was measured bychanging the reference amplitude value of the Viterbi detector.

According to another aspect of the invention, there is provided amagnetic recording and reproduction apparatus wherein a signalprocessing LSI has a function such that at least an input pin of the LSIis designated, through which the reference amplitude value of theViterbi detector is changed.

According to still another aspect of the invention, there is provided amagnetic recording and reproduction apparatus which has the function ofchanging the cut-off frequency of a low-pass filter, the equalizationcoefficient value of a waveform equalizer and the reference amplitudevalue of a Viterbi detector. The degree of data accuracy of the magneticrecording and reproduction apparatus is evaluated by measuring the dataerror rate when the reference amplitude value of the Viterbi detector isdisplaced from a reference value while changing the cut-off frequency ofthe low-pass filter and the equalization coefficient value of thewaveform equalizer.

According to a further aspect of the invention, there is provided amagnetic recording and reproduction apparatus which has the function ofchanging the amount of write precompensation of a write precompensationcircuit and the reference amplitude value of a Viterbi detector. Whilechanging the write precompensation amount of the write precompensationcircuit, the data error rate is measured with the reference amplitudevalue of the Viterbi detector displaced from a reference value. Thus thedegree of data accuracy of the magnetic recording and reproductionapparatus is evaluated.

According to a still further aspect of the invention, there is provideda magnetic recording and reproduction apparatus wherein the writeprecompensation amount of a write precompensating circuit, the cut-offfrequency of a low-pass filter, the equalization coefficient value of awaveform equalizer, and the reference amplitude value of a Viterbidetector are set automatically in accordance with a sequencepredetermined by a coefficient setting sequencer.

According to a yet further aspect of the invention, there is provided amagnetic recording and reproduction apparatus wherein the degree of dataaccuracy of the apparatus is evaluated by measuring the magnitude of asignal obtained by averaging the absolute value or the square value ofthe waveform equalization error.

According to the present invention, the data identification performancecan be deteriorated while maintaining the identification characteristicsof a Viterbi detector of the magnetic recording and reproductionapparatus by displacing the reference amplitude value of the Viterbidetector from a reference value. As a result, a data error occurs withan increasing frequency, thereby making it possible to measure the dataerror rate within a short length of time. The data error rate inherentto the apparatus, i.e., the degree of data accuracy of the apparatus,can thus be predicted from the particular data error rate.

Further, the signal processing LSI has the function of changing thereference amplitude value of a Viterbi detector through an input pin ofthe LSI. As a result, the degree of data accuracy of the apparatus canbe easily evaluated with an LSI built in the apparatus.

Furthermore, the data error rate is measured with the cut-off frequencyof a low-pass filter and the equalization coefficient value of awaveform equalizer changed while displacing the reference amplitudevalue of a Viterbi detector from a reference value. The effect of achange in the reproduction channel parameter on the data accuracy isevaluated, and an optimum value of the parameter can thus be determined.

In addition, according to the invention, the effect of a change in theamount of write precompensation on the degree of data accuracy can beevaluated by changing the write precompensation amount of the writeprecompensation circuit of the magnetic recording and reproductionapparatus and measuring the data error rate with the reference amplitudevalue of the Viterbi detector displaced from a reference value, therebydetermining an optimum value of the write precompensation amount.

Also, the magnetic recording and reproduction apparatus according to theinvention has the function of automatically setting the cut-offfrequency of the low-pass filter, the equalization coefficient value ofthe waveform equalizer and the reference amplitude value of the Viterbidetector in accordance with a sequence predetermined by a coefficientsetting data sequencer. As a result, the degree of data accuracy can beeasily evaluated while setting the coefficient automatically inaccordance with a predetermined sequence without using any externaldevices such as a controller.

What is more, the data identification performance of therecording-reproduction channel can be approximately grasped bymonitoring the signal representing the average of the absolute value orthe square value of the waveform equalization error. As a consequence,the result of a quality assurance test of a product and thechronological change of the recording-reproduction channel including thehead disc when being used by the user after the product shipment can bedetermined.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing the operation for Viterbi detection with thereference amplitude value providing a reference value.

FIG. 2 is a diagram showing the operation with the reference amplitudevalue of the Viterbi detector increased above a reference value.

FIG. 3 is a diagram showing the operation with the reference amplitudevalue of the Viterbi detector decreased below a reference value.

FIG. 4 is a diagram showing the relation between the reference amplitudevalue and the data error rate of a Viterbi detector.

FIG. 5 is a diagram showing a signal processing LSI of a magneticrecording and reproduction apparatus having a coefficient-setting databus.

FIG. 6 is a diagram showing a signal processing LSI of a magneticrecording and reproduction apparatus having a coefficient-setting datasequencer.

FIG. 7 is a diagram showing the main configuration of a magneticrecording and reproduction apparatus according to a first embodiment.

FIG. 8 is a diagram showing the signal operation of each part in a dataerror test conducted using the circuit of FIG. 7.

FIG. 9 is a diagram showing the result of a data error test.

FIG. 10 is a diagram showing a flowchart of a data error test.

FIG. 11 is a diagram showing the configuration of a magnetic recordingand reproduction apparatus according to a second embodiment of theinvention.

FIG. 12 is a diagram showing an example of the equalization error signalprocessing circuit 114 in FIG. 7.

FIG. 13 is a diagram showing an example of the equalization error signalprocessing circuit 114 in FIG. 7

FIG. 14 is a diagram showing an example of the equalization error signalprocessing circuit in FIG. 7.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An embodiment of a magnetic recording and reproduction signal processingcircuit according to the present invention will be described below withreference to the accompanying drawings.

FIG. 1 is a diagram showing the operation of the Viterbi detector, FIG.2 is a diagram showing the operation with the reference amplitude valueof the Viterbi detector increased above a reference value, FIG. 3 is adiagram showing the operation with the reference amplitude value of theViterbi detector decreased below a reference value, and FIG. 4 is adiagram showing the relation between the reference amplitude value ofthe Viterbi detector and the data error rate. The analog reproductionwaveform in FIG. 1 is a waveform input to an A/D converter, and thesample point is a value converted into a digital value by being sampledat an A/D converter and equalized by a waveform equalizer.

In the Viterbi detector, a series of maximum likelihood values areestimated by moving two threshold values as shown in FIG. 1 inaccordance with a series of sample values. The sample value insertedbetween the two threshold values is identified as data “0”. A sampledatum value larger than the first threshold value becomes a candidatefor data “1”, and the sample value smaller than the second thresholdvalue a candidate for data “−1”. In the case of a series where thecandidates for data “1” and data for “−1” appear alternately, data as acandidate become the direct result of identification. In the case wherecandidates of the same polarity successively appear, only the rearcandidate remains as the result of identification, while the frontcandidate is identified as “0”.

The interval between the two threshold values of the Viterbi detector(reference amplitude value: Vth) is usually the same as the expectedvalue of the input waveform amplitude. As shown in FIG. 2, however, aninterval larger than the expected value increases the missing error.When the interval is decreased below the expected value, as shown inFIG. 3, on the other hand, the extra error increases. The relationbetween the reference amplitude value (Vth) and the data error rate(D.E.R) is shown in FIG. 4. In FIG. 4, the ordinate represents the dataerror rate, and the abscissa represents the normalized referenceamplitude value. The relation between the reference amplitude value(Vth) and the data error rate is expressed as a curve (bucket curve) asshown in FIG. 4. The data error inherent to the apparatus can bedetermined by extending the curve and estimating the data error rate forVth=1.0.

FIG. 5 is a diagram showing a signal processing LSI of a magneticrecording and reproduction apparatus having the function of changing thereference amplitude value of a Viterbi detector through acoefficient-setting data bus. A value can be set in a referenceamplitude value register of the Viterbi detector by use of thecoefficient-setting data bus and a register write gate. Thecoefficient-setting data bus may either be in common with a settingroute of registers of other parameters or be provided independently.

FIG. 6 is a diagram showing-a signal processing LSI of a magneticrecording and reproduction apparatus having the function of changing thereference amplitude value of a Viterbi detector by a coefficient-settingdata sequencer. A reference value of the Viterbi detector is set in thecoefficient-setting data sequencer in advance. The sequencer is suppliedwith a sequence start signal and outputs reference amplitude value datafor the Viterbi detector and a register write gate. The output causesthe value of the reference amplitude value register of the Viterbidetector to be set. The reference amplitude value of the Viterbidetector in the coefficient-setting data sequencer may alternatively beset fixedly in the LSI. As an alternative, the reference amplitude valuemay be made changeable by inputting the register value in the sequencerfrom an external source.

FIG. 7 is a diagram showing the configuration of a magnetic recordingand reproduction apparatus according to a first embodiment, FIG. 8 is adiagram showing the signal operation of each part for a data error testconducted by the use of the apparatus in FIG. 7, and FIG. 9 is a graphshowing the result obtained by the data error test.

A signal processing circuit of a magnetic recording and reproductionapparatus according to the first embodiment is shown in FIG. 7. Thissignal processing circuit includes an encode/decode circuit 101, a writeprecompensation circuit 102, a read-write amplifier 103, an AGC circuit104, a low-pass filter 105, an A/D converter 106, a waveform equalizer107, a VFO circuit 108, a Viterbi detector 109, a switch 110, acoefficient-setting sequencer 111, a data generator 112, a datacomparator 113, an equalization error signal processing circuit 114 anda counter 115.

The encode/decode circuit 101 is for converting user data into a codeadvantageous for recording and reproduction. The write precompensationcircuit 102 is for correcting the phase of a write waveform. The datacorrected by the write precompensation circuit is recorded in a magneticrecording medium 11 by a magnetic head 12 through the read-writeamplifier 103. Further, the read-write amplifier 103 amplifies theanalog reproduction waveform signal read by the magnetic head 12 fromthe magnetic recording medium 11. The AGC circuit 104 is for keepingconstant the amplitude of the output waveform signal of the read-writeamplifier 103.

The low-pass filter 105 is for removing high-frequency noise componentsof the analog reproduction waveform signal. The A/D converter 106samples the output signal of the low-pass filter 105 and converts ananalog reproduction waveform signal into a multi-valued digital signal.The waveform equalizer 107 is for shaping the digital waveform signal.The VFO circuit 108 is for generating a sample clock of the A/Dconverter.

The Viterbi detector 109 is for identifying data from the shaped digitalwaveform signal and outputs read data on the basis of the sample clock.The switch 110 is for switching the channel at the time of a data errortest. The coefficient-setting sequencer 111 is for setting in apredetermined sequence the equalization coefficient value of thewaveform equalizer 107, the amount of write precompensation of the writeprecompensation circuit 102, the cut-off frequency of the low-passfilter 105 and the reference amplitude value of the Viterbi detector 109at the time of a data error test. The data generator 112 is forgenerating pattern data at the time of a test.

The data comparator 113 is for comparing the pattern data with the dataidentified by the Viterbi detector 109 and detecting a data read errorat the time of a test. The counter 115 is for counting the number ofdata errors. The data generator 112 has a data register equivalent toabout 36 bits and can freely set a data pattern thereof. The circuitsother than the counter 115 and the read-write amplifier 103 are built inthe recording-reproduction signal processing LSI 110.

In the magnetic recording and reproduction apparatus according to thefirst embodiment, as shown in FIG. 8, for example, at the time of a dataerror test (with the test mode signal of FIG. 8 at “H” level), first,the sequencer 111 sets the first coefficient values (reference amplitudevalue Vth=0.8 of the Viterbi detector, and the equalization coefficientvalue of A), and a data read test is conducted under this condition.Then the data comparator 113 detects a data error and the counter 115counts the number of errors. When the number of data reads reaches apredetermined number of read bits (say, 10⁹ bits), the counter 115 isreset by a coefficient update signal. Also, the coefficient settingsequencer 111 sets the second coefficient value (the reference amplitudevalue of the Viterbi detector Vth=0.9, and the equalization coefficientvalue of A), and a data read test is conducted under this condition.

The result of the data error test obtained in this way including theresult with the equalization coefficient value of B is shown in FIG. 9.The ordinate of FIG. 9 represents a data error rate, and the abscissarepresents the normalized reference amplitude value. The optimumcoefficient value and the corresponding data error rate can bedetermined from this result. In the case under consideration, theequalization coefficient value B with a low data error rate is theoptimum equalization coefficient value. The data error rate can beestimated by extending the curve of the equalization coefficient value Band estimating the data error rate with Vth 1.0.

A flowchart for the data error test is shown in FIG. 10. First, it isdecided whether the coefficient setting sequence has been completed. Ifthe coefficient-setting sequence is completed, the test is finished.Unless the coefficient-setting sequence is completed, arecording-reproduction channel parameter is set. This step is followedby data write, data read, data read error detection and counting of thenumber of errors, in that order. As the next step, it is decided whetherthe number of data read operations has reached a predetermined number ofbits (say, 10⁹ bits). Unless this number of bits is reached, the processreturns to the data read operation. If the number is reached, theprocess is returned to the step of deciding whether thecoefficient-setting sequence providing the first branching point iscompleted.

FIG. 11 is a diagram showing the configuration of a magnetic recordingand reproduction apparatus according to a second embodiment. The signalprocessing circuit of the magnetic recording and reproduction apparatusaccording to the second embodiment includes an encode/decode circuit201, a write precompensation circuit 202, a read-write amplifier 203, anAGC circuit 204, a low-pass filter 205, an A/D converter 206, a waveformequalizer 207, a VFO circuit 208, a Viterbi detector 209, a switch 210,a coefficient-setting sequencer 211, an error detector 213, a datagenerator 214 and a counter 212.

The encode/decode circuit 201 is for converting user data into a codeadvantageous for recording and reproduction. The write precompensationcircuit 202 is for correcting the phase of the write waveform. The datacorrected by the write precompensation circuit is recorded in a magneticrecording medium 21 by a magnetic head 22 through the read-writeamplifier 203. Further, the read-write amplifier 203 amplifies theanalog reproduction waveform signal read by the magnetic head 22 fromthe magnetic recording medium 21. The AGC circuit 204 is for keepingconstant the amplitude of the output waveform signal of the read-writeamplifier 203.

The low-pass filter 205 removes high-frequency noise components of theanalog reproduction waveform signal. The A/D converter 206 is forsampling the output signal of the low-pass filter and converting ananalog reproduction waveform signal into a multi-valued digital signal.The waveform equalizer 207 is for shaping the digital waveform signal.The VFO circuit 208 is for generating a sample clock of the A/Dconverter.

The Viterbi detector 209 is for identifying data from the shaped digitalwaveform signal and outputting read data based on the sample clock. Theswitch 210 is for switching the channel at the time of a data errortest. The coefficient-setting sequencer 211 is for setting theequalization coefficient value of the waveform equalizer 207, the writeprecompensation amount of the write precompensation circuit 202, thecut-off frequency of the low-pass filter 205 and the reference amplitudevalue of the Viterbi detector 209 in accordance with a predeterminedsequence at the time of a data error test. The data generator 214 is forgenerating a data pattern at the time of a test. The data generator 214has a data register of about 36 bits and can set the data patternthereof freely. The error detector 213 is for detecting a data readerror. The counter 212 counts the number of data errors.

According to the second embodiment, a data read error test is conductedusing a disc controller 23 installed outside of the signal processingLSI 20. More specifically, the disc controller 23 instructs the signalprocessing LSI 20 to perform the data write and read operations. Thedisc controller 23 detects an error by means of an error detector 213,and the counter 212 counts the number of errors thereby to detect anerror rate. The error-detecting operation of the error detector 213 maybe performed either by comparison check for each bit or by checking theECC. A test similar to that in the first embodiment can be conducted inthis embodiment to produce a similar result.

According to the first embodiment, a waveform sequalization error isdetermined, which is a difference between an actual waveform equalizedby an equalizer (including nosie generated at the time of recording andreproduction) an ideal value of the waveform not including any noise. Inthis embodiment, the output of the Viterbi detector is assumed to be anideal value for waveform equalization, and the difference between theequalizer output and the output of the Viterbi detector is assumed to bea waveform equalization error. The identification performance of therecording-reproduction channel of the magnetic recording andreproduction apparatus can be coarsely determined by measuring themagnitude of a signal obtained by averaging the absolute value of thewaveform equalization error or the square of the waveform equalizationerror. The resulting identification performance can be used to decide asuccess or not in a product quality assurance test or to evaluate thesecular variation of the recording-reproduction channel of a product inuse. FIGS. 12, 13 and 14 show an example of the equalization errorsignal processing circuit 114 of FIG. 7.

The circuit shown in FIG. 12 includes a subtractor 301, an absolutevalue circuit 302 and an averaging circuit 303, and outputs a digitalsignal of about 6 bits.

The circuit shown in FIG. 13 includes a subtractor 401, an absolutevalue circuit 402, an averaging circuit 403 and D/A converter 404, andoutputs a single analog signal. As compared with the circuit of FIG. 8,the circuit under consideration has the advantage that the output pinscan be reduced to one.

The circuit shown in FIG. 14 includes a subtractor 501, an absolutevalue circuit 502, an averaging circuit 503 and a comparator circuit504, and outputs a 1-bit digital signal. The threshold value of thecomparator 504 is appropriately selected whereby the output signalthereof can be used as a flag for deciding the quality.

Each of absolute value circuits 302, 402, 502 in FIGS. 12, 13, 14 may bereplaced by a square circuit with equal effect.

According to the present invention, the degree of data accuracyincluding the identification characteristics of a Viterbi detector of amagnetic recording and reproduction apparatus can be easily evaluated,thereby making it possible to easily evaluate the dependency of thedegree of data accuracy on the recording-reproduction channel parametersof the apparatus.

What is claimed is:
 1. A data error rate measuring method comprising thesteps of: setting a first equalization coefficient value of a wave formequalizer at a first value which results in a first output wave form ofthe wave form equalizer; carrying out first data read tests inaccordance with the first output wave form; detecting errors in thefirst tests; counting a number of errors generated in the first tests;setting a second equalization coefficient value of the wave formequalizer at a second value which results in a second output wave formof the wave form equalizer; carrying out second data read tests inaccordance with the second output wave form; detecting errors in thesecond tests; counting a number of errors generated in the second tests;and estimating an inherent data error rate from a relation between eachequalization coefficient value and a number of errors associatedtherewith in each respective counting step; wherein the inherent dataerror rate is estimated by extending a first curve and a second curve;wherein said first curve is obtained by data errors generated in thefirst tests; and said second curve is obtained by data errors generatedin the second tests.